Optical trapping and fluorescence control with vectorial structured light

Here we functionalized micro-scaled polymer beads with nano-scaled quantum dots and demonstrate optical trapping and tweezing, with in-situ fluorescence measurement, in an all-digital all-optical configuration. We outline the chemistry required to facilitate this, from deactivating the optical trapping environment to size, adhesion and agglomeration control. We introduce a novel holographic optical trapping set-up that leverages on vectorially structured light, allowing for the delivery of tuneable forms of light from purely scalar to purely vector, including propagation invariant flat-top beams for uniform illumination and tailored intensity gradient landscapes. Finally, we show how this has the potential to quench bleaching in a single wavelength trap by linear (spatial mode) rather than non-linear effects, advancing the nascent field of optics for chemistry.

: The beam profile and cross-section of a flat-top beam a) before the dichroic mirror (DM) and after reflection from the DM b) without a QWP and c) with a QWP added in the setup.

Trap calibration: the equipartition method
An optical trap can be described as a microscopic spring. The particle is kept in the equilibrium position by a harmonic force defined by Hooke's law 1 where F OT is the applied force by the optical trap, κ x is called the trap stiffness in the x-direction and (x − x eq ) the displacement of the particle from the equilibrium position (x eq ). The force in the y-direction can be obtained by considering the displacement in this direction. The resulting trapping potential is given by The equipartition theorem can then be used to measure the trap stiffness. This theorem states that the energy of a system at equilibrium is 1 2 k B T for each degree of freedom, with k B Boltzmann's constant and T the temperature at equilibrium. Therefore, Let σ 2 x = ⟨(x − x eq ) 2 ⟩, the variance of the position of the trapped particle, then Thus by measuring the position variance, the trap stiffness was be determined. The calculation of σ 2 x is straightforward, but requires calibrated position detection which was done using a CCD camera. The position of the particle is needed in units of meters, but since the camera gave the displacement in pixels a conversion is needed. The pixel size of the camera was determined by using an object of known dimensions. The polystyrene sphere with a known diameter of 2 µm was used and the size of a pixel was determined to be 53.3 nm. A temperature of 22 • C and k B = 1.3806 × 10 −23 m 2 kg/s 2 K were used for the trap stiffness calculations. Fig. S2a shows the x-displacement of the particle in a trap over 5 min. The equilibrium position is at x = 0. Fig. S2b shows the corresponding position distribution with a fitted Gaussian curve and S2c the trap potential in units of k B T with a fitted parabolic function, confirming harmonic potential. In Fig. S2d the the potential wells of optical traps at powers of 30 µW, 120 µW and 300 µW are shown -the wells became narrower as the power or trap stiffness increased. Figure S2: Potential analysis of a trapped particle. a) The displacement of the particle centre from the equilibrium position over time and b) the corresponding position distribution and c) potential energy of the trap. d) Comparison of optical trap potential wells at increasing powers of 30 µW, 120 µW and 300 µW.

Comparing flat-top and Gaussian beam traps
From Fig. 4 (main text) we concluded that at the same power, the Gaussian beam will (theoretically) create a stronger optical trap compared to the flat-top beam due to its high peak intensity. This was confirmed experimentally by determining the trap stiffness of these two beams at different powers. Five 2 µm diameter beads were trapped (for 3 min) for each power measurement with both the Gaussian and the flat-top beam. The average trap stiffness of the five beads is plotted in Fig. S3 with the standard error shown by the error bars. From this plot it is clear that the Gaussian beam outperformed the flat-top beam at each power measurement, however, at lower powers the difference in trap stiffness became smaller.

Fluorescence signal from the QD-tagged bead sample
The fluorescence signal from the QD-tagged bead sample, detected with an APD, is shown in Fig. S4 (all measurements were taken with an integration time of 300 ms). The background noise from the QDsample (∼ 2700 counts), shown at times 0-32 s, is due to the presence of unreacted QDs that did not couple to the bead. The fluorescence emission of an optically trapped QD-tagged bead is shown at times 32 -180 s. The QD-tagged bead experienced photobleaching inside the trap, and after ∼ 90 s it was completely bleached. The background signal was subtracted for the results presented in the main text (Fig. 8).

UV-vis absorbance
The absorbance spectrum of the L-cysteine capped QDs is shown in Fig. S6. The broad absorbance spectrum is characteristic of QDs. The two absorption wavelengths indicated on the spectrum were of importance during this study. Firstly, 470 nm was the excitation wavelength used for fluorescence emission monitoring during synthesis and for characterization purposes. The second important wavelength was 532 nm since this was the wavelength of the laser used for excitation in the optical tweezer setup.

Quantum yield
The comparative method was used to determine the quantum yield (Φ QD ) of the QDs using rhodamine 6G (Rh) as the reference. 2,3 where F is the integrated fluorescence intensity, A the absorbance at the excitation wavelength and n the refractive index of the solvent used for the standard Rh sample (std) and the QD sample. Using the Figure S6: UV-vis absorbance of L-cysteine capped CdSe/ZnS QDs in water.
absolute quantum yield of Rh in water (Φ std = 0.90) 4 and n QD = n std = 1.333, the QY of the L-cysteine capped CdSe/ZnS QDs was determined to be 48%.

FTIR analysis
In order to determine the surface chemistry of the QDs and to confirm the success of the ligand exchange reaction, FTIR spectra of the hydrophobic QDs, L-cysteine capped QDs, pure TOPO and L-cysteine were measured -see Fig. S7. All the spectra and peak positions correspond well to reported literature. [5][6][7][8][9][10] The spectrum of TOPO shows peaks at 2918 and 2849 cm −1 corresponding to the symmetric and asymmetric stretching of the CH 2 groups in the alkyl chains. These peaks are also seen in the spectra of the TOPO capped hydrophobic QDs. The characteristic P O and P C stretching of pure TOPO were observed at 1145 and 1464 cm −1 , respectively. The absence of the P O peak in the hydrophobic QDs confirms the coordination of TOPO to the QD surface. The peaks at 1530 and 1434 cm −1 in the hydrophobic QD spectra can be ascribed to the P C stretching of coordinated TOPO. 7 The C O and C O stretches of the carboxylic group in L-cysteine are seen around 1550 and 1390 cm −1 in the L-cysteine capped QDs and the broad peak ∼3200 cm −1 is from the O H stretch. The S H vibration (2550 -2750 cm −1 ) of L-cysteine disappeared in the spectra of the L-cysteine capped QDs confirming covalent bond formation between L-cysteine and ZnS for the CdSe/ZnS QDs and the formation of Cd S in the water-soluble CdSe core QDs. 5 The FTIR analysis verified (along with the other characterization techniques) the successful synthesis of L-cysteine capped CdSe/ZnS QDs. Fig. S8 compares the FTIR spectra of the two starting materials (L-cysteine capped QDs and the polystyrene beads) with the QD-tagged bead product. The spectrum of the product is dominated by the beads with the addition of two new peaks at 1733 and 1220 cm −1 . These peaks can be ascribed to the amide linkage formed between the carboxylic acid on the beads and the L-cysteine on the QDs with the C O stretch corresponding to 1733 cm −1 and C N to 1220 cm −1 . 11-13 Figure S7: FTIR spectra of the hydrophobic and L-cysteine capped core and core/shell QDs as well as the spectra of TOPO and L-cysteine. Figure S8: FTIR spectra of the QD-tagged beads, uncoated commercial beads and L-cysteine capped QDs.